It always holds that \(f_\mu (\alpha )\le \tau _\mu ^*(\alpha )\)  (see, for example, [1]}) and if \(E_\mu (\alpha )\)  is non-empty, then \(\alpha _{\min }\le \alpha \le \alpha _{\max }\)  [2]}.
However, as discussed in the introduction, the set of \(\alpha \)  where \(E_\mu (\alpha )\ne \emptyset \)  need not be a closed interval and, even if it is, the multifractal formalism need not hold [3]}.
